Flickering particles when rendering animation
The problem is with the 'Post processing' settings under render panel.You need to uncheck the sequencer.



Because when the sequencer is checked, it takes into account any videos or image strips already present in the video editor. In your case, you do have a video - most likely a previously rendered video.In such a case, whenever you hit render, instead of rendering the frame again, it simply picks the frame in that video and shows you as render.

You can verify if you have any videos by going into Video Sequence Editor as shown.





Instead of unchecking the sequencer in render settings. You can also delete this video strip to render properly.You can do this by right clicking on it and pressing delete button. You will get an option to 'erase strips'. Click it.



One small suggestion. When you are uploading a blend file here or sharing with someone else please click on 'Pack all into .blend' (as shown below) and save the file before sharing.



This way the textures and files you are using will also be shared in the blend file. In the file you shared, the video and brick textures were not included. This led to delay in figuring out, what the actual problem is. Hope this helps, if not share the blend file again, this time with external data packed.